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              <time title="创建时间：2019-12-31 13:18:25" itemprop="dateCreated datePublished" datetime="2019-12-31T13:18:25+08:00">2019-12-31</time>
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            <p>在学习的过程中经常要做些笔记，记在笔记本上的话非常不方便的查阅。如果只是记日记，记录下每天都做了啥，那用纸质的笔记本还好; 但对于学习笔记要经常整理以及归纳，就得需要经常改动及查阅。<br>最近有发现一款非常不错的做笔记的软件Marginnote，目前只有iOS/Mac的版本，没有Android的版本。<br>这款软件可以很方便的在pdf文件上做标记，并且将pdf中的关键字，句子摘录出来，制作成思维导图。让我想起了大师李敖的读书方法，李敖每读一本书，会将书拆的很碎，把经典的句子都从书上剪下来，把剪下来的句子分类整理到自己的册子里，这样自己日后在写作的时候从相关的册子里之间找自己要的东西就好了。</p>
<p>下图为一个处于学习模式的marginnot的snapshot：</p>
<ul>
<li>总共分为三块：左边为摘录出来的文字的一个逻辑关系；中间为根据左边文字的逻辑关系生成的思维导图；右边为原文；</li>
<li>用户可以调节左边摘录文字的逻辑关系（父子关系？兄弟关系？），同时中间的思维导图也会跟着变；</li>
<li>点击左边的摘录文字，右边的原文会自动跳转到该文字所在的位置。而且这些摘录的文字可以在右边原文中选用不同的颜色。</li>
</ul>
<p><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/MarginNote/marginnote-overview.png" alt="Marginnote" title="overview"></p>

          
        
      
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            <p>  第一次看到这个比较新鲜精确的概念：<strong>纯时间</strong>与<strong>毛时间</strong><br>  比如你说你一天上班工作的时间是8小时，但实际上只有2小时是真正在工作的，其他时间可能在做无意义的发呆或是刷微信。那这8小时就是工作的毛时间，2小时就是工作的纯时间。<br>这个概念是在<a href="https://book.douban.com/subject/1115353/">《奇特的一生》</a>这本书里提到的，在豆瓣上评分还挺高。作者描述了俄罗斯科学家柳比歇夫的时间统计法，用日期+事件+花费时间的方式来记录自己一天所做的事情，并坚持了56年，没有一天断过。柳比歇夫在每周，每月，每年都对自己记录的时间做总结，看哪项事件用了多久，可以精确到分钟。这样有个好处是自己对时间的估算是非常精确的。除了做总结，柳比歇夫还对自己一生的时间做五年规划，每过五年，他就把度过的时间和干过的事分析一通，可以说是做个总的鉴定，总结能客观公正的反映过去一年的历史，抓住变化无常的老想溜掉的日常生活，抓住我们没有擦觉到的损失掉的不知去向的时间。<br>  他能准确的感知时间，精确到1分钟，对他来说，时间的急流事看得见，摸得着的，他仿佛置身于这急流之中，觉得出来光阴冷冰冰的流逝。<br>  然而对于没有远大目标的人来说，这个方法很难坚持下去，坚持也不见得有意义。<br>  我自己每天会做日记记录做了那几件事情，但是还没有做过总结，只是对比下去年同一天在干啥，看起来还挺有意思的。看了这本书有一种豁然开朗的感觉，原来还有记录这么细致的日记，而且对自己的时间剖析的这么认真。 </p>

          
        
      
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            <p>看到一个很有意思的<a href="http://www.magi.com">搜索引擎</a>，在搜索结果出来的时候还做个summary，虽然没啥用，但是还挺有新意，也许未来能做的更好。</p>
<p><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/%E5%85%B6%E4%BB%96%E6%96%87%E4%BB%B6/magi-search.png" alt="magi"></p>

          
        
      
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            <p>mark一下一个online的编译环境： <a href="https://code.labstack.com">https://code.labstack.com</a></p>

          
        
      
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            <p>规范 Vol2 的Part E，讲HCI command的第7章有几个command，看起来很有用，这里list下</p>
<h1 id="7-5-1-Read-Faild-Contact-Counter-command"><a href="#7-5-1-Read-Faild-Contact-Counter-command" class="headerlink" title="7.5.1 Read Faild Contact Counter command"></a>7.5.1 Read Faild Contact Counter command</h1><p><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/BluetoothBaseband/Bluetooth_HCI_7.5.1_FailedContactNumber.png" alt="ReadFailedContactCounterCommand"><br>这个计数器(Failed_Contact_Counter，两个字节)是用来记录由于flush timeout到期（一般是因为空气中信号干扰比较多，数据包重传比较多）而flush掉的数据包的个数，在做bt music的时候经常看到smartphone送过来的数据包的序列号不连续，如果smartphone有用这个command来monitor数据包的状况的话，就比较容易看到这个现象。</p>
<blockquote>
<p>When the 802.11 PAL receives an HCI_Read_Failed_Contact_Counter command it shall return the number of consecutive incidents in which the remote device didn’t respond after the flus&gt;h timeout had expired, and the L2CAP packet that was currently being transmitted was automatically flushed. The Failed Contact Counter is specific to each logical link.</p>
</blockquote>
<h1 id="7-1-47-Truncated-Page-command"><a href="#7-1-47-Truncated-Page-command" class="headerlink" title="7.1.47 Truncated Page command"></a>7.1.47 Truncated Page command</h1><p><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/BluetoothBaseband/HCICommand-7.1.47.png" alt="Trncated Page"><br>可以用来探测目标设备在不在可连接范围内？</p>
<blockquote>
<p>The HCI_Truncated_Page command is used to page the BR/EDR Controller with the specified BD_ADDR and then abort the paging sequence after an ID response has been received. See [Vol &gt;2] Part B, Section 8.3.3 for additional information.</p>
</blockquote>
<p>复习下page的几个步骤，请看下面的两张图：</p>
<p><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/BluetoothBaseband/Baseband-Page-steps_list.png" alt="Page step list"><br><img src="https://wnnwoo.oss-cn-chengdu.aliyuncs.com/BluetoothBaseband/Baseband-page-message-sequence.png" alt="Page step message sequence"></p>
<p>BLUETOOTH CORE SPECIFICATION Version 5.1 | Vol 2, Part E page 1112</p>

          
        
      
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            <p>本文来自 <a href="https://blog.csdn.net/crazy_scott/article/details/79293576">https://blog.csdn.net/crazy_scott/article/details/79293576</a>  感谢原作者。</p>
<p><strong>安装插件</strong></p>
<ol>
<li>首先我们需要安装Mathjax插件</li>
</ol>
<blockquote>
<p>npm install hexo-math —save</p>
</blockquote>
<p>2 更换Hexo的markdown渲染引擎，hexo-renderer-kramed引擎是在默认的渲染引擎hexo-renderer-marked的基础上修改了一些bug，两者比较接近，也比较轻量级。</p>
<blockquote>
<p>npm uninstall hexo-renderer-marked —save<br>npm install hexo-renderer-kramed —save</p>
</blockquote>
<p><strong>解决语义冲突</strong></p>
<p>由于LaTeX与markdown语法有语义冲突，在markdown中，斜体和加粗可以用<em>或者_表示，在这里我们修改变量，将_用于LaTeX，而使用</em>表示markdown中的斜体和加粗。<br>在博客根目录下，进入node_modules\kramed\lib\rules\inline.js，把第11行的escape变量的值做相应的修改：</p>
<blockquote>
<p>//escape: /^\([\`<em>{}[]()#$+-.!_&gt;])/,<br>escape: /^\([`</em>[]()#$+-.!_&gt;])/,</p>
</blockquote>
<p>这一步是在原基础上取消了对,{,}的转义(escape)。<br>同时把第20行的em变量也要做相应的修改:</p>
<blockquote>
<p>//  em: /^\b_((?:__|[\s\S])+?)_\b|^*((?:**|[\s\S])+?)*(?!*)/,<br>em: /^*((?:**|[\s\S])+?)*(?!*)/,</p>
</blockquote>
<p><strong>更改配置文件</strong></p>
<p>这里是最重要的一步，我找了好久才在这个网站中找到适用的解决办法。<br>进入到主题目录，找到_config.yml配置问题，把mathjax默认的false修改为true，并更换cdn的url，具体如下：</p>
<p># MathJax Support<br>mathjax:<br>  enable: true<br>  per_page: true<br>  #cdn: //cdn.bootcss.com/mathjax/2.7.1/latest.js?config=TeX-AMS-MML_HTMLorMML<br>  cdn: //cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML</p>
<p>如果配置文件里已经有这一行而且版本比这行还新的话，就可以不用更新。</p>
<p><strong>写博客</strong></p>
<p>在每次需要用LaTeX渲染的博文中，在文章的Front-matter里启动mathjax，具体如下：</p>
<p>-—<br>title: Hexo Usage<br>date: 2018-2-8 21:01:30<br>tags: Hexo<br>mathjax: true<br>-—</p>
<p><a href="https://blog.csdn.net/ethmery/article/details/50670297">Mathjax 语法</a><br><a href="https://blog.csdn.net/weixin_43159148/article/details/88621318">Markdown/LaTex数学符号大全</a></p>

          
        
      
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            <p>TRNG（True Random Number Generator）是真随机数生成器。<br>真随机数生成器通常是通过放大电路的热噪声来产生随机数，温度高于绝对零度的原子都存在热运动，在集成电路里这些原子的热运动会在电路里产生噪声，噪声会使得电路中的电压存在微小的起伏，TRNG就是通过放大这些微小的起伏来产生随机数。<br>不过TRNG也有不少缺点。</p>
<ul>
<li>首先就是产生随机数的速度很低，因为噪声放大电路有低通特性，使得高频的噪声被滤除了，而放大低频噪声就需要较长的时间，使得TRNG的工作频率受限。</li>
<li>其次是电路系统里有很多不同的噪声，但并不是所有噪声都是随机的，比如电源噪声中很大一部分就是和系统时钟强相关的。而TRNG是一个放大极小信号的电路，它对外界干扰是极其敏感的，为了避免外界非随机信号的干扰TRNG必须要耗费不少功率和面积在屏蔽上。由于面积和功耗限制，CPU中不能内置很多个TRNG；由于频率限制，单个TRNG输出的随机数数量有限，这使得单靠TRNG产生的随机数数量不足以满足系统需要。</li>
</ul>
<p>还有用其他方法来生成随机数的，比如有个网站专门提供生成随机数的服务<a href="https://www.random.org">Random</a>，该网站的随机数来自大气噪声（atmospheric noise）。<br><a href="https://www.random.org/randomness/">关于真随机数和伪随机数</a></p>

          
        
      
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            <p>伽罗华（法国，1811～1832）才华横溢，可惜在21岁时早早死于情场决斗。他证明了：对于给定的一个素数次不可约方程能判断出它是否能根式求解。<br>Bluetooth在bit streaming过程中计算Sync word，HEC，FEC及data whitening时使用到了伽罗华域中的计算规则来处理比特流，本文就收集到的信息做个总结。</p>
<p>一个元素个数有限的域称为<strong>有限域</strong>，或者<strong>伽罗华</strong>域(Galoisfield)</p>
<ol>
<li>有限域中元素的个数为一个素数，记为GF(p),其中p为素数;<blockquote>
<p>一个大于1的整数，如果它的正因数只有1和它本身，就叫做素数，否则就叫做合数</p>
</blockquote>
</li>
<li><p>有限域中运算满足<br>– 交换律:a+b = b+a, a·b = b·a<br>– 结合律:(a+b)+c = a+(b+c), a·(b·c) = (a·b)·c<br>– 和分配律:a·(b+c) = a·b+a·c</p>
<p>将GF(p)延伸为一个含有$p^m$个元素的域，称为GF(p)的扩展域，表示为GF($p^m$)，m是一个非零正整数。</p>
<blockquote>
<p>注意:GF(p)是GF($p^m$)的子集。</p>
</blockquote>
</li>
</ol>
<p>二进制域GF(2)是扩展域GF($2^m$)的一个子域，类似于实数域是复数域的一个子域一样。除了数字0和1之外，在扩展域中还有特殊的元素，用一个新的符号a表示。GF($2^m$)中任何非0元素都可由a的<strong>幂次</strong>表示。</p>
<p>有限元素的集合GF($2^m$)，只能含有$2^m$个元素，并且对乘法封闭，其约束条件为$a^{(2^m−1)}$+1=0<br>• 根据这个多项式限制条件，任何幂次等于或超过$2^m-1$的域元素都可降阶为下述幂次小于$2^m-1$的元素:</p>
<script type="math/tex; mode=display">a^{(2^m+n)} = a^{(2^m−1)}a^{(n+1)} = a^{(n+1)}</script><p>这样，GF($2^m$)的元素可表示为:</p>
<script type="math/tex; mode=display">GF(2^m) ={0,a^0,a^1,a^2,...,a^{2^m −2}}</script><p>扩展域$GF(2^m)$中的加法<br>• 在$GF(2^m)$中，将每个非0域元素用多项式$a_i(x)$表示，其系数至少有一个不为0。对于i=0,1, 2,…,$2^m-2$，有:</p>
<script type="math/tex; mode=display">a_i = a_i(x) = a_{i,0} + a_{i,1}x + a_{i,2}x^2+...+a_{i,m-1}x^{m-1}</script><p>• 先看m=3,有限域表示为$GF(2^3)$,下表为上式描述的基本元素(Primitive Element) ${x^0,x^1,x^2}$映射为7个元素{$a_i$}和一个0元素。表中的各行是二进制数字序列，代表上式中的系数$a_{i,0}、a_{i,1}、a_{i,2}$的取值。</p>
<div class="table-container">
<table>
<thead>
<tr>
<th>_</th>
<th style="text-align:center">$x^0$</th>
<th style="text-align:center">$x^1$</th>
<th style="text-align:center">$x^2$</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td>$a^0$</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td>$a^1$</td>
<td style="text-align:center">0</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td>$a^2$</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td>$a^3$</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td>$a^4$</td>
<td style="text-align:center">0</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td>$a^5$</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td>$a^6$</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td>$a^7$</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
</tr>
</tbody>
</table>
</div>
<p>多项式$f(x)=1+x+x^3$ 为GF($2^3$)的元素与基本元素之间的映射。</p>
<p>有限域中两个元素的<strong>加法</strong>定义为两个多项式中同幂次项系数 进行<strong>模2加</strong>，即<br>$a^i+a^j=(a_{i,0}+a_{j,0}) + (a_{i,1}+a_{j,1})x + … + (a_{i,m-1}+a_{j,m-1})x^{m-1}$<br>• 有限域的<strong>本原多项式</strong>。本原多项式定义了域GF($2^m$)， 一个多项式是本原多项式的充要条件:</p>
<blockquote>
<p>一个m阶的不可约多项 式f(x)，如果f(x)整除$x^n+1$的最小正整数n满足$n=2^m-1$，则该多项式是本原的。</p>
</blockquote>
<h3 id="关于多项式在伽罗华域的求根"><a href="#关于多项式在伽罗华域的求根" class="headerlink" title="关于多项式在伽罗华域的求根"></a>关于多项式在伽罗华域的求根</h3><p> 以$p(x) = 1 + x + x^3$ 为例，多项式的幂次为m=3,所以由p(x)所定义的域中包含了$2^m=2^3=8$个元素。求解p(x)的根就是指找到x 使p(x)=0。由高斯的基本代数学理论我们知道，对于幂次为m的多项式必然有m个根。对于这个例子，p(x)=0有3个根，由于这3个根不可能位于与p(x)系数相同的有限域中，而是位于扩展域GF($2^3$)中。<br>用扩展域的元素 a来定义多项式p(x)的根，可写成如下形式:p(a)=0<br>即 $1+a+a^3=0$，在该多项式两边都加上 1 + a, 就可以得到$a^3=1+a$ 这意味着$a^3$可以表示为更低阶a项的加权和。</p>
<p>类似地有:<br>$a^4$=a<em>$a^3$=a</em>(1+a)=a+$a^2$<br>$a^5$=a<em>$a^4$=a</em>(a+$a^2$)=$a^2$+$a^3$=1+a+$a^2$<br>$a^6$=a<em>$a^5$=a</em>(1+a+$a^2$)=a+$a^2$+$a^3$=1+$a^2$<br>$a^7$=a<em>$a^6$=a</em>(1+$a^2$)=a+$a^3$=1=$a^0$ </p>
<p>所以，有限域GF($2^3$)的8个元素为 ${0,a^0,a^1,a^2,a^3,a^4,a^5,a^6}$</p>
<p>这8个元素中哪些是p(x)=0的3个根呢?我们可通过枚举 找到!<br>p($a^0$)=1, $a^0$不是<br>p($a^1$)=1+a+$a^3$=0, $a^1$是<br>p($a^2$)=1+$a^2$+$a^6$=1+$a^0$=0, $a^2$是<br>p($a^3$)=1+$a^3$+$a^9$=1+$a^3$+$a^2$=1+$a^5$=$a^4$, $a^3$不是<br>p($a^4$)=1+$a^4$+$a^12$=1+$a^4$+$a^5$=1+$a^0$=0, $a^4$是<br>同理可计算p($a^5$)、p($a^6$)都不等于0，所以p(x)=1+x+$x^3$的 3个根是a, $a^2$, $a^4$</p>
<p>主要参考文献有<br><a href="https://cloud.tencent.com/developer/article/1005808">FEC的介绍</a></p>

          
        
      
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